Osmotic Pressure Measurements of
Phase-Separating Protein Solutions
by
Arya Akmal
S.B., Massachusetts Institute of Technology
(1 989)
Submitted to the Department of Physics
in Partial Fulfillment of
the Requirements for the Degree of
Master of Science in Physics
at the
Massachusetts Institute of Technology
September 1990
Q Massachusetts Institute of Technology, 1990
Signature of Author
Department of Physics
June, 1990
Certified by
_
George B. Benedek
Professor of Physics
Thesis Supervisor
Accepted
by
,
_.
_
George F. Koster
Chairman, Departmental Committee
MAtISACH.LSEiTS
INSTIUTE
OFTECHNO0.OG
Y
SEP 111990
LIBRARIES
ARCHIVES
1
Osmotic Pressure Measurements of
Phase-Separating Protein Solutions
by
Arya Akmal
Submitted to the Department of Physics on June 30th, 1990
in Partial Fulfillment of the Requirements for the Degree of
Master of Science in Physics
Abstract
Measurements of the osmotic pressure of aqueous solutions of
Bovine y-crystallin and of chicken-egg-white lysozyme were made
as a function of solute concentration at T=20+1 °C. The equation of
state for solutions of each of these proteins, of the form fll=f(c,T),
was thus traced along this isotherm for protein concentrations up to
225 mg/ml. Osmotic pressure measurements were performed using
a dynamic osmometer of our own design, which eliminated the long
equilibration times characteristic of static osmometry.
Values for the osmotic compressibility, a/ac,
of y-crystallin
were determined via static light scattering. These measurements are
compared to the n(c) data.
The protein solutions were modeled as a gas of attracting rigid
spheres. The osmotic pressure data are compared to the predictions
2
of a model which includes a rigid sphere interaction as well as an
attractive interaction quadratic in protein volume fraction.
Thesis Supervisor: Dr. George B. Benedek
Title: Alfred H. Caspary Professor of physics and Biological Physics
3
Introduction
When aqueous solutions of certain globular proteins are cooled
below their coexistence curve two distinct liquid phases of different
protein concentrations appear. The phenomenon of liquid-liquid
phase separation in aqueous solutions of biological macromolecules
has been the subject of growing interest in recent years. Liquid-liquid
phase separation was observed in solutions of lysozyme by Ishimoto
and Tanaka1 . This behavior was also noted in solutions of
mammalian eye-lens yll-crystallins2 and subsequently implicated in
the formation of cold-induced cataracts. The proposed mechanism
for cold cataract formation is based on the fact that the different
phases have different indeces of refraction. At the onset of phase
separation, microscopic regions of different concentrations are
present in solution. Light passing through regions with varying
indeces of refraction is randomly scattered, the result is opacity of the
solution 3 .
Liquid-liquid phase separation is a consequence of the
underlying microscopic interactions among solution components.
Phase separation is a macroscopic manifestation of a net solutesolute interaction. A thorough understanding of the nature of solvent-
4
solvent, solvent-solute and solute-solute interactions is essential to
an understanding of the macroscopic phenomenon of phase
separation. Osmotic pressure measurements represent a simple and
convenient means of investigating molecular interactions in solution.
One early investigation of a biological macromolecule via
osmometry was the study of aqueous solutions of haemoglobin by
Adair 4 , 5. More recently, Prouty, Schecter and Parsegian6 performed
osmotic pressure measurements on haemoglobin, and on the phaseseparating protein lysozyme. Osmotic pressure studies of calf-lens
extracts, namely a-crystallins and phase-separating y-crystallins
were carried out by Veretout, Delaye and Tardieu7 and by Veretout
and Tardieu8 .
Osmotic pressure measurements provide a direct means of
characterizing a system in terms of an equation of state,
=I-l(c,T).
An ideal solution, made up of non-interacting components, is
described by the van t'Hoff equation of state:
H=RT
(M)n
where R is the gas constant, T is the temperature, <M> n is the
number average molecular weight of the solute and c is the solute
5
concentration in units of solute mass over total volume. This
description of a solution is analogous to the ideal gas description of a
real gas, in that only entropic contributions to the osmotic pressure
are accounted for.
Although such a description is approximately
valid for dilute solutions, real solutions exhibit deviations from ideal
behavior due to energetic interactions. The deviations from ideality
apparent in the equation of state of a system are therefore a direct
measure of these interactions.
In this paper we present a simple, yet accurate method to
perform osmotic pressure measurements. We have performed a
check on the validity of this method by comparing the measured
values of [(c) for bovine yll-crystallin to corresponding values for
aIl/ac determined via static light scattering. We have attempted to
account for the observed deviations from ideal behavior, by
introducing volume-exclusion and attractive interaction corrections to
the van t'Hoff equation of state.
6
Materials and Methods
Preparation of samples
Samples of chicken-egg-white lysozyme protein were obtained
from Sigma chemical corporation, St Louis, MO (Grade ill, lot #
65F-8220). The lysozyme samples were dissolved in phosphate
buffer with a pH of 6.8 and ionic strength of 0.6M (0.1M sodium
chloride, 0.5M sodium phosphate, 0.02% sodium azide).
These
buffer conditions were chosen to yield a critical temperature of 0 ° C
for the protein solutions9.
Dissolved 50ml samples were dialyzed
twice against 4L volumes of phosphate-saline buffer to remove low
molecular-weight contaminants.
Dialysis tubing
(Spectrapore
Medical Industries, Los Angeles, CA) with a nominal molecular
weight cutoff of 10,000 daltons was used in this process.
The
dialyzed samples were then centrifuged at approximately 30,000g
and concentrated to the appropriate values in a stirred concentrator
(model 8050, Amicon corp.,Danvers, MA) with a 5,000 dalton
molecular-weight cutoff membrane (Amicon YM5 membrane).
Bovine yll-crystallin samples were obtained from calf lenses as
described by Bjork1 0 and by Thomson2 .
The total monomeric
proteins were separated from calf lens homogenate extract via size
7
exclusion chromatography. Crude yll-crystallin was then separated
from the total y-crystallin via cation-exchange chromatography. The
samples obtained in this manner were dialyzed exhaustively against
a pH 7.05, 0.1 M phosphate buffer (with 0.02% sodium Azide to retard
bacterial growth). These samples were then concentrated to the
required values with a 10,000 molecular-weight cutoff membrane
(Amicon YM10). Both the lysozyme and yll-crystallin samples were
stored at room temperature to retard formation of protein crystals2 .
Experimental procedure
Osmotic pressures were
determined by
making a
null
measurement. A chamber containing the sample and a chamber
containing pure solvent were separated by a membrane permeable
only to the solvent. Under such conditions, solvent flows into the
sample chamber due to the difference in the chemical potential of the
solvent across the membrane.
The measurement consists of
detecting the solvent flow across the membrane and applying a
hydrostatic pressure to the sample chamber in order to stop the flow.
The applied hydrostatic pressure which stops the solvent flow is the
osmotic pressure of the solution.
We have employed two methods to detect solvent flow across
8
the membrane. One method to achieve this is to watch the rise or
drop of fluid level in a thin transparent
tube separated
from the
sample chamber by the membrane1 1 . The tube then acts as the
solvent reservoir. A more accurate means of detecting flow is
illustrated in figure 1. As indicated in the schematic, fluid flowing from
the sample chamber into the solvent reservoir passes through a
length of fine tubing 0.127mm in diameter and 150.4cm in length
(Rainin corp, Woburn, MA). According to Poiseuille's law of fluid flow,
a pressure developes between the ends of the tubing according to
the following relationship:
AP= Li
4"r4
where r is the radius of the tubing, L is the length of the tubing, r is
the viscosity of the fluid, and I is the volume flux of the fluid. A
pressure transducer (model PX160, Omega Engineering, Stamford,
CT) placed between the two ends of tubing produces a voltage
proportional to the Poisseuille pressure, which is in turn proportional
to the flow of solvent through the tubing. This setup permitted
detection of flows as little as 0.011l1/s.
Measurements of osmotic pressure were made at 20+10°Cas
follows: a measured volume of protein solution was placed in a
9
Amicon ultrafiltration cell. An equal volume of buffered solvent was
placed in an identical cell connected to the first cell across a
semipermeable membrane and a length of fine tubing. The level of
fluids in the two chambers was carefully balanced. The balancing
was achieved by first placing equal amounts of solvent alone, in the
two chambers and adjusting the relative heights of fluids in the
chambers such that no flow occured between them. All the solvent
was then removed from one chamber and replaced with an identical
volume of sample. This insured that a difference in fluid levels did not
contribute to the hydrostatic pressure balancing the osmotic pressure
across the membrane.
The flow of solvent between the two chambers, indicated by the
voltage across the transducer, was observed on a chart recorder.
The sample chamber was then pressurized with nitrogen gas until
this voltage matched the no-flow voltage(see fig.1). The transducer
voltage output level corresponding to no flow past the membrane
was repeatedly checked by isolating the transducer from the flow by
means of valves located at its terminals.
A cellulose membrane with a 5,000 dalton molecular weight
cutoff (Amicon YM5) was used for the lysozyme osmotic pressure
10
measurements. The measurements of yll-crystallin osmotic pressure
were carded out with a similar cellulose membrane with a 10,000
dalton molecular weight cuttoff (Amicon YM10).
The sample concentrations were determined by measuring their
ultraviolet absorbances, using a Hewlet Packard 8451A diode array
spectrophotometer. Absorbances were determined by comparing the
intensity of radiation of a given wavelength transmitted through a
sample to the intensity of radiation transmitted through a reference
solution. Three dilutions, typically of 5 gl of the sample in 3 ml buffer,
were made at each concentration. The absorbance at 280nm of each
dilution was measured, and the average of the three values was
used to determine the concentration of the sample. The specific
0.
1%,lcm for lysozyme
absorbtion coefficient, A28o
is 2.6412. This
number represents the absorbance at 280nm of a 1mg/ml solution,
through
a
1cm
optical
path.
We
have
used
a
value
of
A2 80 0.1%lcm=2.4 for y1l-crystallin13. Reported values for this quantity,
however, range from 2.010 to 2.814.
Values of aIl/ac were determined at T=20.1+0.1°C
via static
light scattering from y-crystallin samples at concentrations of 40.2
mg/ml, 79.8 mg/ml and 104.9 mg/ml. These data were obtained on a
11
spectrometer based on the design by Haller, Destor and Cannell1 5.
aruacis
related to the Rayleigh ratio, R(6), at a scattering angle 0=0
via the following themodynamic relationship, valid for binary
mixtures 1 6:
all/ac= kB7T[4 2 n 2(dn/dc) 2 /X0 4 ]C[ 1/R(0)]
where c is the concentration
of protein in g/cm 3 , and R(0) is the
Rayleigh ratio at scattering angle 0=0. The
refractive index
increment, dn/dc, was determined using a Bausch & Lomb Abbe-3L
refractometer, by measuring the index of refraction of samples at a
series of yll concentrations, and performing a linear least squares
fit(see figure 2). dn/dc was found to be 2.4cm3 /g.The Rayleigh ratio
can be calculated from the scattered light intensity in the following
manner:
R()=
(|))/l
-(-)
2Rref
(!ref
(o)/It)
ref
The experiment consisted of measurements of the ratio of
scattered intensity to transmitted intensity from samples in 10mm
diameter cylindrical
cells. The ratio
(Iscattered/transmitted)was
measured at five scattering angles between 36.90 and 105.20. The
measurement procedure, described by Chamberlin1 7 , reduced
inaccuracies due to drifts in laser power and photomultiplier tube
12
response, corrected for
sample turbidity,
and provided dust
discrimination. A vertically polarized argon-ion laser at X=488nm was
employed as a light source.
The water bath, with nref=1.333 and Rref=2.51x10-6 cm '1 , was
used as the reference in determination of R(0)1 6 . R(e=0) was
determined by averaging the measured R(O) values, as this quantity
exhibited no 0 dependence. The accuracy of these measurements is
supported by previous studies1 6 which showed no evidence of
multiple scattering.
13
Results and Analysis
We have made measurements of osmotic pressure as a
function of solute concentration, for solutions of lysozyme
yll-crystallin up to their critical concentrations (-244mg/ml).
and
These
data, which appear in tables 1, 2 and 3 and in figure 3, show
significant deviations from ideal behavior. The osmotic pressures we
have measured are below the van t'Hoff law (see fig.7), revealing
strong attractive interactions, which cause phase-separation.
The osmotic pressure data for yll-crystallin are in good
agreement with values of
anlacwe
have measured via static light
scattering. Line segments representing these measured slopes have
been superimposed on the osmotic pressure data in figure 3. The
measured values of a/ac
appear in table 4. The final value in this
table, at a concentration of 244mg/ml, is taken from Schurtenberger
et al.1 6 The value reported by Schurtenberger et al. assumed a value
for dn/dc of 2.0cm3 /g. We have measured dn/dc to be 2.4cm3 /g. The
al/ac quoted in table 4 has been recalculated using this new value
for dn/dc.
Osmotic pressure measurements are generally employed to
determine solute molecular weight, or more specifically solute
14
number-average molecular weight, <M>n , by appliying the Van't Hoff
to data in the dilute regime. The data presented is not particularly
well suited for such analysis, as the majority of points lie in a
concentration regime, where non-idealities are significant.
The
validity of the data can still be checked by this method, however. We
have made least-square polynomial fits to IVc vs c plots, and taken
the (rl)=o predicted by these fits to be the slope of 11(c) in the dilute
regime. According to the van t'Hoff law, this sope is proportional to
RT/<M>n. The
number-average mulecular weights
were thus
determined using the following relationship:
RT
(rlc)c=o
A second-order fit to the y1 data, appearing in fig.4, yields
(/c)c=o
= 1.185x106erg/g, which corresponds to a molecular weight
of 20,550. A linear fit to data below 80mg/ml (fig.5) yields (c)c=O =
1.240x106 erg/g, corresponding to a molecular weight of 19,640.
Both values are in good agreement
with the accepted value of
20,00010. A second-order fit to lysozyme data below 100mg/ml (from
Akmal, S.B.thesis) predicts a molecular weight of 14,390 , compared
to a literature value of 14,40018.
15
A comparison of the inter-molecular interactions in solutions of
these two proteins can be made by plotting both sets of data on
molecular weight-independent axes, as in figure 7. In this figure, the
horizontal axis represents volume fraction,
= vsp c. Where the
specific volume, vsp, was taken to be 0.703cm3/g for lysozyme
0.71cm3 /g for y
20 .
calculated from the
19
and
The specific volume of solute, vsp, can be
solution density, p, using the following
relationship:
/p = (Vsp-Vsolvent)Wsolute+Vsolvent
where vsolventis the reciprocal of the solvent density, and Wsoluteis
the weight fraction of solute.
The vertical axis in figure 7 represents a normalized, molecular
weight-independent osmotic pressure, rIVhs/kT. Vhs in this equation
is the 'hard-sphere volume' of an individual protein, defined as:
Vhs
V MW
NA
where vsp is the protein specific volume in cm3/g , MW is the protein
molecular weight and NA is Avogadro's number. Vhs is calculated to
be 1.68x10-20 cm 3 for lysozyme and 2.36x10-20 cm 3 for yll using the
previously quoted values for specific volumes and the accepted
molecular weights. Thus, with the dependence on molecular weight
16
removed, features of the data related to energetic interactions can be
explicitly displayed. The van t'Hoff law appears as a line of slope one
in these units:
nv,
kT=
Non-idealties appear as deviations from the line of slope one.
The two data'sets display surprisingly similar features on these axes.
This implies very similar intermolecular interactions for solutions of
proteins with significantly different isoelectric points, in different
solvent environments. The critical temperature T c, and the critical
concentration c c appear to be the important parameters which
determine the behavior of these solutions. It is therefore significant
that the two protein solutions studied here have the same critical
concentration, and that their critical temperatures differ by only
5.50 C.
The energetic interactions should exhibit dependence on
T- T,
solution temperature. The reduced temperature, T S is a useful,
Tc-normalized
quantity to consider in this analysis.
The critical
temperature of the lysozyme solutions is at T=O0°C 9, whereas the
yll solutions have a critical temperature T=5.5 0 C 2. The lysozyme
17
solutions in this study were therefore at a slightly higher reduced
temperature and should exhibit greater osmotic pressures. When
plotted on the normalized axes of figure 7, the data do in fact display
evidence of such a dependence on reduced temperature. A slight
difference in the normalized osmotic pressures of lysozyme
and
ll-crystallin solutions is evident at protein volume fractions above
12%.
As mentioned previously, appropriate corrections to the van
t'Hoff equation of state can be made to account for the observed
behavior of our solutions. Specifically, corrections can be made for
the short-range repulsive interactions, due to the finite size of the
solution components, and for the long-range attractive interactions
which lead to phase separation. The system in question can be
modeled as a gas of attractive rigid spheres.
An accurate calculation of the first five virial coefficients of the
(non-attracting) hard sphere interaction has been made by Ree and
Hoover 2 1 :
NkT 1 +4y+ 10y2 + 18.36y3 +28.2y 4 +39.2y 5 +...
NkT
where the volume fraction y is defined as
.-
F2(VV), V0 being the
18
volume occupied by the spheres when closely packed in a facecentered cubic lattice. The following closed form, developed by
Carnahan and Starling2 2, reproduces the integer part of these virial
coefficients when expanded in a Taylor series:
PV 1+y+y2 _y3
(l-y) 3
NkT
Working by analogy to a gas of attracting rigid spheres, the osmotic
pressure can be expressed in terms of this non-attracting rigidsphere interaction plus an appropriate attractive potential:
nVhs
1+(+02-D3
kT
(1-03]
-This
to
expression
the
is
van off+law ...)
to first-order in
2 equal[(c
This expression is equal to the van t'Hoff law to first-order in
added terms in powers of
4.
The
represent the attractive potential
responsible for phase-separation. The gas volume fraction, y, defined
above has been replaced in this expression, by the previously
defined solute volume fraction, . The latter quantity is appropriate in
a description of a system containing more than one species: namely
a solution which contains both solute and solvent molecules.
The simplest attractive potential of the form above is quadratic
in protein volume fraction (cn=Ofor n>2). Values may be obtained for
19
c by applying the condition
c2 , and for the critical volume fraction
dJI,
det
as-V a- =' O at the critical point. The chemical potential of the solvent,
s,
is related to the osmotic pressure via
specific volume of the solvent, and
Vs=lgs-i-s0 , where Vs is the
s ° is the solute concentration
independent part of the chemical potential. A value of 10.60 is
obtained for c 2 in this manner 2 3 .
Tc
A value of 9.98 is obtained for Tc 2 by making a fit to the
y1l-crystallin data. The value predicted by the model is 10.08 for
Tc=278.5K and T=293K.
c2 .
The best fit to the lysozyme data yields a value of 9.76 for
The value predicted by the model is 9.88 for Tc=273 K and T=293.
The one-parameter quadratic fits of the form: const. x , were
made to the difference between the measured points and the noninteracting rigid-sphere potential, I-measured-excluded
volume-
The
resulting fits to the yll -crystallin and lysozyme data appear in figures 8
and 9.
20
Conclusions
Osmotic pressure measurements represent a straight-forward
means of measuring microscopic interactions in solution. The simple
osmometer described in this paper is a powerful tool for the
investigation of these interactions.The validity of the results we
present here is supported by the molecular weight predictions for
yll-crystallin and lysozyme, which are in excellent agreement with the
accepted values. The osmotic pressure measurements are also in
very good
agreement with values
compressibility, alIc,
obtained for the
osmotic
measured via light scattering.
We have demonstrated that the phase behavior of solutions of
each of the two proteins is well described by a simple attracting rigidsphere model. The success of this model in describing the behavior
of these solutions indicates that these systems can be characterized
using macroscopically measurable quantities such as the critical
concentration and the critical temperature.
Lysozyme
and
y-crystallin
have
significantly
different
microscopic properties. Under the conditions of this investigation,
lysozyme carries a considerable net charge9 , whereas y"l-crystallin
carries only a small net charge. Despite this difference, the same
21
equation of state succesfully describes both systems. Both proteins
investigated here have the same critical concentration. The critical
temperature, however, can be easily altered by changing solution
conditions such as pH and ionic strength. Future work in this area
should involve investigation of these proteins under a variety of
solution conditons in order to test the universality of a simple
equation of state of the type proposed, for phase-separating globular
proteins.
22
Table
1 :Osmotic
of
pressure
yll-crystallin
solutions
T=20± 1°C
Concentration, [mg/ml]
Osmotic Pressure, [ 104 dyne/cm2 ]
28.43±0.44
3.00±0.48
30.86±0.37
3.30
"
39.29±1.6
3.94
4.53
"
"
58.57±0.38
72.29±0.47
75.86±0.49
108.57±0.66
132.57±0.89
142.29+0.75
151.57±0.17
159.29±3.84
5.22 "
6.48"
7.66 "
8.62"
9.23
"
9.49
9.65
"
"
205.71±+3.13
10.1
218.29±4.46
11.2
"
Table2: Osmotic pressure of lysozyme solutions
T=20+ 1°C
Concentration, [mg/ml]
23.14±0.20
46.86±0.49
71.86±0.59
74.29±0.64
117.29±2.44
135.57±2.20
146.14±0.15
188.57+ 1.22
OsmoticPressure, [10 4 dyne/cm2 ]
2.91 ±0.48
5.58 "
7.53 "
7.53 "
197.71±+0.45
15.4 "
17.7 "
225.00±2.30
10.9
12.3
"
13.1
16.1
23
Table 3: Osmotic pressure of lysozyme solutions
from ref.[11]
T=22.5± 1.5°C
Concentration, [mg/ml]
7.36±0.03
Osmotic Pressure, [10 4dyne/cm2 ]
1.22±0.05
8.23 ±0.09
1.30±0.04
9.25±0.08
1.53±0.15
9.93±0.11
1.35±0.05
1.50±0.10
1.75 "
1.99
2.79
10.42±0.06
12.13±0.18
15.14±0.19
19.29±0.05
21.00±0.08
22.71 +0.13
23.14±0.25
27.71±0.18
29.00 ±0.33
31.14±0.20
33.29±0.64
40.00±0.25
41.00+0.32
45.29±1.46
50.71±0.36
58.57+0.59
2.91
3.06
3.18
3.59+0.20
3.52±0.10
3.54 "
4.03"
4.30
4.90±0.20
4.64±0.10
5.34±0.10
6.07±0.15
66.57±0.76
6.75±0.15
72.29± 0.24
6.82±0.15
7.09±0.10
73.71±+0.23
24
Table 4: Osmotic compressibility of yll-crystallin
solutions
T=20.0±0.1°C
Conc., [mg/ml]
40.2 ±0.3
79.8 ±0.7
104.7±0.9
244
I(O)r,,/,(o))
(1.58 ± 0.04) x 10-3
(4.17 ± 0.04) x 10-4
(2.29 ± 0.07) x 10 ' 4
anl/ac, [1 0 5 cm 2 /s 2 ]
7.16
3.75
2.70
1.0*
* Taken from Schurtenberger et al.1 6 , recalculated using new dn/dc
25
pressure
release
N2
V supply
stirrer
membrane
solution
Applied pressure readout
1,
V supply
pressure
transducer
rsuc
output
to chart recorder
solvent flow
Figure 1:
It
Schematic of experimental apparatus
-
fine tubing
26
index of refraction of gamma II solutions
1.355
a
1.350
o
X
1.345
om
1.340
1.335
0
20
40
60
80
100
concentration [mg/ml]
Figure 2:
The index of refraction of yll-crystallin as a function of
concentration. The linear fit yields a value of 2.4 for dn/dc.
27
Osmotic pressure of gamma II and lysozyme solutions
~~~~~~~~~~..........-,,,I,.....
27
0
150000
0·
0
0
2 100000
a.
0
00
E
o
_
50000
O0
I .
0
.
.
I.
50
=
*
I .
.
. .
100
... I ,
150
.
...
I
.
.
.
.
200
c (mg/ml)
Figure 3:
Filled circles- Lysozyme osmotic pressure, open circlesLysozyme osmotic pressure from ref.[1 1], filled squares- Yll osmotic
pressure, line segments- an/ac
data obtained via static light
scattering. The line segments have been vertically positioned to
permit easy comparison to osmotic pressure data.
I
250
28
H/c vs c for gamma II
_
I
_
I
-
.
-
.
.
-
-
I
.
_ __
.
.
.
.
-
-
.
I
_ __
.
.
I
.
-I
-
_ __
.
.
1200
1000
-
C
a
800
-
3i
600
0
-
.
- -
50
-
. ... .
- -
I
-
.
-
-
I- . -.
150
100
- . -
-
200
-.. -
-I
-
250
c (mg/ml)
Figure 4:
Second-order fit to fl/c vs c for yal. Intercept yields a value of
20,550 for the molecular weight.
29
fl/c vs c for gamma II
I
I
I
'
I
'
I
'
I
1200
91000
C
800
600
I
0
.
I
20
.
I
.
I
60
40
.
I
80
.
I
100
c (mg/ml)
Figure 5:
Linear fit to i/c vs c for yll at concentrations< 80 mg/ml.
Intercept yields a value of 19,640 for the molecular weight
30
Il/c vs c for lysozyme
___
I
__
I
__
I
__
__
I
1600
cD
E
1400
oU3
0.
A.
1200
0
E
0
1000
0
I
,
0
.
.
I
20
..
.
I
40
c (mg/ml)
.
.-
I
.
.
60
Figure 6:
Second-order fit to fl/c vs c data for lysozyme at concentrations
below 100 mg/ml. Intercept yields a value of 14,390 for the molecular
weight.
.
31
0.14
0.12
f
0
0.10
- o.08
o
0.06
0.04
0.02
0.00
0.00
0.05
0.10
volume fraction
0.15
Figure 7:
Osmotic pressure of yll and lysozyme on normalized, molecular
weight independent axes.
Filled circles- lysozyme (Tc=0OC), filled
squares- yll (T=5.5 0 C), Solid line- van t'Hoff law, valid for noninteracting solution components. Overlap of the two data sets
indicates similar interactions in both systems
32
Osmotic pressure of gamma 11solutions
-r
I
·
-·
1
.
*
-·
*
.~~~~~~~~~
--
·
I
--
T
-r
.
.
..L
l
--
0.06
GE
a
0.
0.04
P
cu
*
'g
'5.:
0.02
0.00
I
I
0.00
0.05
0.10
volume fraction
Figure 8:
One-parameter fit to yl 1-crystallindata
-
0.15
,
33
Osmotic pressure of lysozyme solutions
_
0.08
__
I
I
1
I
I
.
I
·
+
0.06
t-
0.04
-
*o
0
K5
0.02
-
0.00
....
0.00
....
I
I
0.05
0.10
..
.
0.15
volume fraction
Figure 9:
One-parameter fit to lysozyme data. Open circles represent
data taken from reference [11].
34
References
[1]
Ishimoto, C. & Tanaka, T.
Critical behavior of a binary mixture of protein and salt water.
Phys. Rev. Lett. 39:474-477, 1977.
[2]
Thomson, J.A., Schurtenberger, P., Thurston G.M., &
Benedek, G.B.
Binary liquid phase separation and critical phenomena in a
protein/water solution.
Proc. Natl. Acad. Sci. USA 84:7079-7083,
1987.
[3]
Benedek, G.B.
Theory of transparency of the eye.
Applied Optics 10:459-473, 1971.
[4]
Adair, G.S.
A critical study of the direct method of measuring the osmotic
pressure of haemoglobin.
Proc. Royal Soc. London 108:627-637, 1925.
[5]
Adair, G.S.
Theory of partial osmotic pressures and membrane equilibria,
with special reference to the application of Dalton's law to
Haemoglobin solutions in the presence of salts.
Proc. Royal Acad. London 120:573-603, 1928.
[6]
Prouty, M.S., Schecter, A.N. & Parsegian, V.A.
Chemical potential measurements of deoxyhemoglobin S
polymerization: determination of the phase diagram of an
assembling protein.
J. Mo. Biol. 184:517-528, 1985.
[7]
Veretout, F., Delaye, M. & Tardieu, A.
Molecular basis of eye-lens transparency: Osmotic pressure
and x-ray analysis of a-crystallin solutions.
J. Mol. Biol. 205:713-728, 1989.
[8]
Veretout, F. & Tardieu, A.
The protein concentration gradient within eye-lens might
originate from constant osmotic pressure coupled to
differential interactive properties of crystallins.
Eur. Biophys. J. 17:61-68, 1989.
35
[9]
Taratuta, V.G., Holschbach, A., Thurston, G.M., Blankschtein,
D. & Benedek, G.
Liquid-liquid phase separation of aqueous lysozyme
solutions: Effects of pH and salt identity.
J. Phys. Chem. 94:2140-2144, 1990.
[10]
Bjork, .
Studies on ycrystallin from calf lens II. Purification and some
properties of the main protein components.
Exp. Eye Res. 3:254-261, 1964.
[11]
Akmal, A.
An experimental determination of an equation of state for
phase-separating protein solutions: The osmotic pressure
of lysozyme..
Bachelors' Thesis, Massachusetts Institute of Technology,
1989.
[12]
Canfield, R.E.
Peptides derived from tryptic digestion of egg white lysozyme.
J. Biol. Chem. 238:2691-2697, 1963.
[13]
Thomson, J.A.
Unpublished.
[14]
Pierscionek-Balcerzak,
B., Smith, G. & Augusteyn, R.C.
The refractive increments of bovine a- - and t-crystallins.
Vision Res. 27:1539-1541,
[15]
1987.
Haller, H.R., Destor, C., Cannell, D.S.
Photometer for quasi-elastic and classical light scattering.
Rev. Sci. Instrum. 54:973-983, 1983.
[16]
Schurtenberger, P., Chamberlin, R.A., Thurston, G.M.,
Thomson, J.A. & Benedek, G.B.
Observation of critical phenomena in a protein-water solution.
Phys. Rev. Lefft. 63:2064-2067,
[17]
1989.
Chamberlin, R.A.
Light scattering studies on lecithin micellar solutions.
PhD thesis, Massachusetts Institute of Technology,
Manuscript in preparation.
36
[18]
Kurachi, K., Sieker, L.C. & Jensen, L.H.
Structures of Triclinic Mono- and Di-NAcetylglucosamine:Lysozyme complexesAcrystallographic study.
J. Mol. Biol. 101:11-24, 1976.
[19]
Sophianopoulos, A.J., Rhodes, C.K., Holcomb D.N. & Van
Holde, K.E.
Physical studies of lysozyme.
J. Biol. Chem. 237:1107-1112,
[20]
1962.
Measured using a Mettler/PaarDMA 602/60 digital density
meter, by C.R. Middaugh at the University of Wyoming.
[21]
Ree, F.H. & Hoover, W.G.
Fifth and sixth virial coefficients for hard spheres and hard
disks.
J. Chem. Phys. 40:939-950, 1964.
[22]
Carnahan, N.F. & Starling K.E.
Equation of state for nonattracting rigid spheres.
J. Chem. Phys. 51:635-636, 1969.
[23]
Kondo, M.
Determination of crystal formation line in an aqueous solution
of a lens protein.
Master's thesis, Massachusetts Institue of Technology, 1989.
Acknowledgements
I would first and foremost like to thank Michael Broide, whose
contributions to this work cannot be underestimated. If it weren't for
his technical expertise, boundless scientific enthusiasm and excellent
(albeit warped) sense of humor, this thesis would probably not have
been realised. I would also like to thank light-scatterrer extraordinaire,
Bernard Fine, whose competence and down-to-earth easy-going style
added a whole new dimension to this work, virtually at the last
moment. I am grateful to George Thurston, who provided much needed
guidance at every stage of this project.
Jayanti Pande, Ian Shand-Kovach, Carolyn Berland, James Melhuish and
Genevieve Sparagna have all been special friends, whose willingness to
lend a sympathetic ear and occasional, all-too-necessary application of a
kick in the pants is much appreciated.
Ty Ogun deserves
thanks for his efficient delivery of the large amounts
of protein required for this experiment, as does Richard Chamberlin for
his light-scattering apparatus.
Finally, I would like to thank Professor George Benedek,
generous financial support made it all possible.
whose